Using stochastic optimization methods for stock selling decision making and option pricing: numerics and bias and variance dependent convergence rates

Abstract

This paper is concerned with using stochastic approximation and optimization methods for stock liquidation decision making and option pricing. For stock liquidation problem, we present a class of stochastic recursive algorithms, and make comparisons of performances using stochastic approximation methods and that of certain commonly used heuristic methods, such as moving averaging method and moving maximum method. Stocks listed in NASDAQ are used for making the comparisons. For option pricing, we design stochastic optimization algorithms and present numerical experiments using data derived from Berkeley Options Data Base. An important problem in these studies concerns the rate of convergence taking into consideration of bias and noise variance. In an effort to ascertain the convergence rates incorporating the computational efforts, we use a Liapunov function approach to obtain the desired convergence rates. Variants of the algorithms are also suggested.